In most of the blocks a button is a separate element, which you can delete without affecting the block as a whole.

1. Hover over the button in the block and click on the three dots:

2. Choose Delete in the drop-down list:

3. If you have a couple of buttons in the row, hover over the buttons and click on the “gear” to access the element settings:

4. In the pop-up window click on the basket icon to delete the needed button:

5. Publish the site for the changes to appear live.